SYDNEY—Australia on Wednesday selected Dutch oil-and-gas consulting firm Fugro NV to lead a rebooted search for Malaysia Airlines Flight 370 in the southern Indian Ocean.

The selection follows a month-long tender process that also attracted bids from groups that specialize in recovering wrecks from deep water, including previous efforts to locate the Titanic in the mid-1980s and an Air France jetliner that crashed in the mid-Atlantic...